For the moment, we are in position to discuss the qualitative flow diagram around the Gaussian fixed point. First of all, note that all the coefficients of the beta function of the system (REF ) are not negative definite. This fact seems to be a special feature of this model, meaning that the weight of the anomalous dimension does not dominate the vertex contribution. This fact is a first difference with respect to the similar non-Abelian \(\phi ^6\)  model studied in [1]}. However, the analysis providing in this reference remains true, and the model is not asymptotically free. We will not repeat the complete analysis given in [1]} , but a qualitative argument is the following. Exploiting the fact that the hyperplans \(\bar{\lambda }_2=0\)  and \(\bar{\lambda }_3=0\)  are invariant under the flow, we can look at only a two-dimensional reduction of the complete system (REF ). We choose \(\bar{\lambda }_2=0\) , and plot the numerical integration of the reduced flow equation in Figure (REF ) (on the left) below.
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